Answer:
Explanation:
To solve the equation |5-4r| = 17, we need to consider two cases:Case 1: 5 - 4r is positiveIf 5 - 4r is positive, then we have:5 - 4r = 17Subtracting 5 from both sides, we get:-4r = 12Dividing both sides by -4, we get:r = -3So if 5 - 4r is positive, then the solution to the equation is r = -3.Case 2: 5 - 4r is negativeIf 5 - 4r is negative, then we have:-(5 - 4r) = 17Simplifying the left side by distributing the negative sign, we get:-5 + 4r = 17Adding 5 to both sides, we get:4r = 22Dividing both sides by 4, we get:r = 5.5So if 5 - 4r is negative, then the solution to the equation is r = 5.5.Therefore, the solution set of the equation |5-4r| = 17 is {-3, 5.5}.To show this solution set on a number line, we can draw a number line and mark the points -3 and 5.5 with open circles, since these values are not included in the solution set. Then, we shade the part of the number line between -3 and 5.5, since any value of r in this interval satisfies the equation. The resulting number line looks like this:
So the solution set of the equation is the interval (-3, 5.5).